A body of mass M moving with velocity u suddenly explodes into two fragments. If a fragment of mass m comes to rest, then find the Q value of explosion.

Solution

Let v be the velocity of second fragment of mass (M – m).
According to law of conservation of momentum,
Mu = (M- m) v

rightwards double arrow space straight v space equals space open parentheses fraction numerator straight M over denominator straight M space minus space straight m end fraction close parentheses straight u

Kinetic energy of mass M before explosion is,
K₁= 1/2 Mu²
Kinetic Energy after explosion is,
K₂ =

1 half left parenthesis space straight M space minus space straight m right parenthesis thin space straight v squared space equals space 1 half left parenthesis space straight M space minus space straight m right parenthesis space open parentheses fraction numerator straight M over denominator straight M space minus space straight m end fraction straight u close parentheses squared

equals space open parentheses fraction numerator straight M over denominator straight M space minus space straight m end fraction close parentheses space 1 half M straight u squared Now comma space straight Q space value space equals space straight K subscript 2 space minus space straight K subscript 1 space equals space open parentheses fraction numerator straight M over denominator straight M space minus straight m end fraction close parentheses space 1 half Mu squared space minus space 1 half Mu squared space equals 1 half open parentheses fraction numerator mM over denominator straight M space minus straight m end fraction close parentheses space straight u squared

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